TY - JOUR
T1 - Analytical investigation of the bias effect in variance-type estimators for inference of long-range dependence
AU - Krunz, Marwan
AU - Matta, Ibrahim
N1 - Funding Information:
Dr. Krunz is a recipient of the National Science Foundation CAREER Award (1998–2002). He currently serves on the editorial board for the IEEE/ACM Transactions on Networking, the Computer Communications Journal, and the IEEE Communications Interactive Magazine. He was the Technical Program Co-chair for the 9th Hot Interconnects Symposium (Stanford University, August 2001). He serves as the Publicity Co-chair for the ACM/IEEE MOBICOM 2002 and the IEEE INFOCOM 2003 Conferences. He has served as the Tutorial Co-chair for the IEEE INFOCOM 2001, the Panel Chair for the IEEE IPCCC 2000 Conference, and the Panel Co-chair for the IEEE INFOCOM ’99 Conference. Dr. Krunz has served and continue to serve on the technical program committees of many international conferences. He is a member of IEEE and ACM.
Funding Information:
The work of M. Krunz was supported by the National Science Foundation under grants ANI 9733143, CCR 9979310, and ANI 0095626. The work of I. Matta was supported by the National Science Foundation under grant ANI 0095988.
PY - 2002/10/22
Y1 - 2002/10/22
N2 - Since the publication of the Bellcore measurements in the early nineties, long-range dependence (LRD) has been in the center of a continuous debate within the teletraffic community. While researchers largely acknowledge the significance of the LRD phenomenon, they still disagree on two issues: (1) the utility of LRD models in buffer dimensioning and bandwidth allocation, and (2) the ability of commonly used statistical tools to differentiate between true LRD and other potential interpretations of it (e.g., non-stationarity). This paper is related to the second issue. More specifically, our objective is to analytically demonstrate the limitations of variance-type indicators of LRD. Our work is not meant to advocate a particular modeling philosophy (be it LRD or SRD), but rather to emphasize the potential misidentification caused by the inherent bias in variance-type estimators. Such misidentification could lead one to wrongly conclude the presence of an LRD structure in a sequence that is known to be SRD. Our approach is based on deriving simple analytical expressions for the slope of the aggregated variance in three autocorrelated traffic models: a class of SRD (but non-Markovian) M/G/∞ processes, the discrete autoregressive of order one model (SRD Markovian), and the fractional ARIMA process (LRD). Our main result is that a variance-type estimator often indicates, falsely, the existence of an LRD structure (i.e., H > 0.5) in synthetically generated traces from the two SRD models. The bias in this estimator, however, diminishes monotonically with the length of the trace. We provide some guidelines on selecting the minimum trace length so that the bias is negligible. We also contrast the VT estimator with three other estimation techniques.
AB - Since the publication of the Bellcore measurements in the early nineties, long-range dependence (LRD) has been in the center of a continuous debate within the teletraffic community. While researchers largely acknowledge the significance of the LRD phenomenon, they still disagree on two issues: (1) the utility of LRD models in buffer dimensioning and bandwidth allocation, and (2) the ability of commonly used statistical tools to differentiate between true LRD and other potential interpretations of it (e.g., non-stationarity). This paper is related to the second issue. More specifically, our objective is to analytically demonstrate the limitations of variance-type indicators of LRD. Our work is not meant to advocate a particular modeling philosophy (be it LRD or SRD), but rather to emphasize the potential misidentification caused by the inherent bias in variance-type estimators. Such misidentification could lead one to wrongly conclude the presence of an LRD structure in a sequence that is known to be SRD. Our approach is based on deriving simple analytical expressions for the slope of the aggregated variance in three autocorrelated traffic models: a class of SRD (but non-Markovian) M/G/∞ processes, the discrete autoregressive of order one model (SRD Markovian), and the fractional ARIMA process (LRD). Our main result is that a variance-type estimator often indicates, falsely, the existence of an LRD structure (i.e., H > 0.5) in synthetically generated traces from the two SRD models. The bias in this estimator, however, diminishes monotonically with the length of the trace. We provide some guidelines on selecting the minimum trace length so that the bias is negligible. We also contrast the VT estimator with three other estimation techniques.
KW - Hurst parameter estimation
KW - Pseudo self-similarity
KW - Variance time plot
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U2 - 10.1016/S1389-1286(02)00305-5
DO - 10.1016/S1389-1286(02)00305-5
M3 - Article
AN - SCOPUS:0037159150
SN - 1389-1286
VL - 40
SP - 445
EP - 458
JO - Computer Networks
JF - Computer Networks
IS - 3
ER -